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In this paper, a new full-rate space-time block code (STBC) possessing a quasi-orthogonal (QO) property is proposed for QAM and 8 transmit antennas. This code is designed by serially concatenating a real constellation-rotating precoder with the Alamouti scheme. The QO property enables a maximum likelihood (ML) decoding to only require joint detection of four groups of real symbols at a receiver. Hence, this code has an identical and greatly reduced ML decoding complexity with the conventional minimum decoding complexity QO-STBC (MDC- QO-STBC) and the Xian's QO-STBC, respectively. Especially, the proposed QO-STBC is guaranteed to enjoy full diversity for general QAM unlike the existing MDC-QO-STBC presented for only QPSK. By simulation results, we show that the proposed code exhibits the identical and slightly degrade error performance with the existing MDC-QO-STBC for 4-QAM and the Xian's QO-STBC for 4 and 16-QAM, respectively.